Question

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with the probability 0.2 then $P(A) + P(B) = $?

• A. \( 0.4 \)
• B. \( 1.2 \)
• C. \( 0.8 \)
• D. \( 1.4 \)

Hint:

Remember the formula for the probability of the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. You can rearrange this formula to find the sum of individual probabilities.

Answer 1

The Correct Option is C

We are given the probability that at least one of the events A and B occurs, which is $P(A \cup B) = 0.6$. We are also given the probability that A and B occur simultaneously, which is $P(A \cap B) = 0.2$. We know the formula for the probability of the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ We need to find $P(A) + P(B)$. Rearranging the formula: $P(A) + P(B) = P(A \cup B) + P(A \cap B)$ Substituting the given values: $P(A) + P(B) = 0.6 + 0.2 = 0.8$ Thus, $P(A) + P(B) = 0.8$.